STRUCTUHAL UNITS IN t'ELLlTLAK PHYSIOLOGY 



201 



has a minimum at a definite distance of 

 equilibrium. Tlie ]iliysieal si<iiiificaiice of 

 this equilibrium depends, however, on the 

 energy inyolved. For two spherical i)ar- 

 ticles of the dimensions of a large protein 

 molecule, diameter 100 A, this minimum is 

 of the order of 0.1 of the thermal energy, 

 and consequently no e(inilil)rium results, 

 the total etfect of the forces being to pre- 

 vent agglutination. The situation is very 

 different, however, with larger particles 

 and especially with elongated, needle- or 

 plate-like particles. In this case the en- 

 ergy of equilibrium may be much greater 

 than h-T, with the result that a stable ecjui- 

 librium occurs at ordinary temperatures. 



4- 



Fk;. 2r. Two similar i);trtick'.s close together; 

 repulsive forces. 



This was first observed in tobacco-mosaic 

 virus, where the long particles maintain 

 themselves in a regular hexagonal array 

 (Fig. 2), even down to dilutions of about 

 2 per cent dry matter; that is, when the 

 particles are 800 A apart. In the case of 

 flat particles the equilibrium is even more 

 stable. The existence of these forces fur- 

 nishes an explanation for the iridescent 

 ferric-hydroxide gels, which consist of flat 

 particles in equidistant layers that may be 

 as much as 5,000 A apart, or of the order 

 of the wave length of visible light, so that 

 their regularities give an effect similar to 

 that of butterfly wings. These long-range 

 Langmuir-Levine forces are extremely 

 sensitive to changes in the concentration 

 or pH of the medium, and here we have a 

 mechanism ideally suited for the develop- 

 ments of easily transformable fluid and 

 yet definite structures such as w^e observe 

 in living cells. 



A characteristic feature of these forces is 

 the appearance of spindle-shaped bodies, 



usually called factoids (Fig. 2). The shape 

 of a factoid depends on the existence of 

 orientation of the long particles on a free 

 surface, and thus on the ])roduction of a 

 surface tension which is different in the 

 two directions of that surface. The shape 

 can be ({nantitatively accounted for on this 

 h3"pothesis. Roughly it nui.y be said that 

 the spindle shape depends on the relative 

 ease with which the surface can be bent on 



Fiii. ID. Potential fimctiou, Urdiiiates, potential 

 IT ; abscissas, distances r. 



an axis parallel to the long direction of the 

 particles compared with that of bending it 

 along the axis perpendicular to them. 

 Such factoids have been often observed in 

 living structures, the most striking case 

 being that of the spindle found at certain 

 stages of mitosis. Pfeiffer was the first to 

 suggest that this spindle is probably a fac- 

 toid, and that the fibers of which it is nor- 

 mally supposed to be composed are arte- 

 facts formed by the dehydration action of 

 the fixing medium. The study of tobacco- 

 mosaic factoids confirms this suggestion; 

 in this case, also, fibers are formed which 



